Question

A surge of $20kV$ magnitude travels along a lossless cable towards its junction with two identical lossless overhead transmission line. The inductance and the capacitance of the cable are $0.4mH$ and $0.5\mu F$ per km. The magnitude of the voltage at the junction due to surge is

• A. 36.72 kV
• B. 18.36 kV
• C. 6.07 kV
• D. 33.93 kV

Answer 1

The correct option is D 33.93 kV

Where, $Z_1=Z_2$
Parameter of cable:
Inductance $=L_C=0.4mH/km$
and
Capacitance

$=C_C=0.5\mu F/km$

Surge impedance of the cable$=Z_C$

$\sqrt{\frac{L_C}{C_C}}=\sqrt{\frac{0.4\times {10}^{-3}}{0.5\times {10}^{-6}}}=28.28\Omega$

Parameters of Over Head Transmission lines

Inductance, $L_1=1.5mH/km$

Capacitance, $C_1=0.015\mu F/km$

Surge impedance of the line$=Z_1=Z_2$

$=\sqrt{\frac{L_1}{C_1}}=\sqrt{\frac{1.5\times {10}^{-3}}{0.015\times {10}^{-6}}}$

$=316.22\Omega$

$E=20kV$

Junction voltage$=E_j$

$=\frac{2E\times \frac{1}{Z_C}}{\frac{1}{Z_C}+\frac{1}{Z_1}+\frac{1}{Z_2}}$

$=\frac{2\times 20\times \frac{1}{28.28}}{\frac{1}{28.28}+\frac{2}{316.22}}$

$=33.93kV$